Permutations and Combinations Quiz Set 004

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Question 1

How many four letter words, with all the letters different, can be formed out of the letters of the word 'BACKGROUND'?

 A

5040.

 B

5050.

 C

5030.

 D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

Solution | Discuss! | Chapters»

Question 2

What is the value of 5P3?

 A

60.

 B

70.

 C

50.

 D

80.

Soln.
Ans: a

5P3 is ${5 !}/{(5 - 3) !}$ = 60.

Solution | Discuss! | Chapters»

Question 3

6 men are standing in front of 7 cabins. In how many ways can they enter the cabins?

 A

5040.

 B

5045.

 C

5038.

 D

5041.

Soln.
Ans: a

The first has 7 options, the second has (7 - 1), and so on. This is expressed as 7P6, which evaluates to 5040.

Solution | Discuss! | Chapters»

Question 4

There are 3 trains between two stations A and B. In how many ways can a student go from A to B and return by a different train?

 A

6.

 B

11.

 C

4.

 D

7.

Soln.
Ans: a

The upward journey is possible in 3 ways, and the downward in 2 ways. So the outcomes are 3 × 2 = 6.

Solution | Discuss! | Chapters»

Question 5

In how many ways can 2 letter words be formed by using a given set of 13 consonants?

 A

156.

 B

161.

 C

154.

 D

157.

Soln.
Ans: a

The first place can get any of the 13 consonants, the second place can then get (13 - 1), and likewise. This is expressed as 13 × 12, which evaluates to 156.

Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-05-08

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